The Smallest Perturbation of a Submatrix that Lowers the Rank of the Matrix
George A. Watson · IMA Journal of Numerical Analysis · 1988
The problem is considered of determining, for a rectangular matrix T, the smallest perturbation of a given submatrix that lowers the rank of T. For different classes of matrix norms, it is shown how the solution of the problem can be obtained through an equivalent, often simpler, problem.